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Defects in the hexagonal boron nitride (h-BN) layer can facilitate the tunneling current through thick h-BN tunneling barriers. We have investigated such current-mediating defects as local probes for materials in two dimensional heterostructure stacks. Besides IV characteristics and negative differential conductance, we have characterized the electrical properties of h-BN defects in vertical graphene-h-BN-Cr/Au tunnel junctions in terms of low frequency current noise. Our results indicate a charge sensitivity of 1.5×10-5 e/Hz at 10 Hz, which is equal to good metallic single electron transistors. The noise spectra at low frequency are governed by a few two-level fluctuators. For variations in the electrochemical potential, we achieve a sensitivity of 0.8 μeV/Hz.